Geometry Section 10.1

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AC a. SOLUTION is a radius because C is the center and A is a point on the circle. AC a.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. b. AB SOLUTION b. AB is a diameter because it is a chord that contains the center C.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. DE c. SOLUTION c. DE is a tangent ray because it is contained in a line that intersects the circle at only one point.

EXAMPLE 1 Identify special segments and lines Tell whether the line, ray, or segment is best described as a radius, chord, diameter, secant, or tangent of C. AE d. SOLUTION d. AE is a secant because it is a line that intersects the circle in two points.

EXAMPLE 2 Find lengths in circles in a coordinate plane Use the diagram to find the given lengths. a. Radius of A b. Diameter of A Radius of B c. Diameter of B d. SOLUTION a. The radius of A is 3 units. b. The diameter of A is 6 units. c. The radius of B is 2 units. d. The diameter of B is 4 units.

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and draw them. a. b. SOLUTION a. 4 common tangents 3 common tangents b.

EXAMPLE 3 Draw common tangents Tell how many common tangents the circles have and draw them. c. SOLUTION c. 2 common tangents

Assignment 1 of 2 #3-10 all, 13-17 odd, page 655

EXAMPLE 4 Verify a tangent to a circle In the diagram, PT is a radius of P. Is ST tangent to P ? SOLUTION Use the Converse of the Pythagorean Theorem. Because 122 + 352 = 372, PST is a right triangle and ST PT . So, ST is perpendicular to a radius of P at its endpoint on P. By Theorem 10.1, ST is tangent to P.

Find the radius of a circle EXAMPLE 5 Find the radius of a circle In the diagram, B is a point of tangency. Find the radius r of C. SOLUTION You know from Theorem 10.1 that AB BC , so ABC is a right triangle. You can use the Pythagorean Theorem. AC2 = BC2 + AB2 Pythagorean Theorem (r + 50)2 = r2 + 802 Substitute. r2 + 100r + 2500 = r2 + 6400 Multiply. 100r = 3900 Subtract from each side. r = 39 ft . Divide each side by 100.

Find the radius of a circle EXAMPLE 6 Find the radius of a circle RS is tangent to C at S and RT is tangent to C at T. Find the value of x. SOLUTION RS = RT Tangent segments from the same point are 28 = 3x + 4 Substitute. 8 = x Solve for x.

Assignment 2 of 2 #19-25 odd, page 656